Cantor Confusion
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From: Virgil on 5 Dec 2006 17:04 In article <4575B9F3.7080107(a)et.uni-magdeburg.de>, Eckard Blumschein <blumschein(a)et.uni-magdeburg.de> wrote: > > Reals according to DA2 are fictitious No one mathematically competent who is at all familiar with Cantor's 2nd proof finds any such thing falsehoods in it. It is EB who is fictitious.
From: Ralf Bader on 5 Dec 2006 18:55 Bob Kolker wrote: > Eckard Blumschein wrote: >> an exact numerical representation available. Kronecker said, they are no >> numbers at all. Since the properties of the reals have to be the same as >> these of the irrationals, all reals must necessarily also be uncountable >> fictions. > > For the latest time. Uncountability is a property of sets, not > individual numbers. There is no such thing as an uncountable real > number. Nor is there any such thing as a countable integer. Countability > /Uncountability are properties of -sets-, not individuals. > > You have been told this on several occassions and you apparently are too > stupid to learn it. These people (Blumschein and Mückenheim) don't know how words and notions are used in mathematics. Blumschein takes a word, e.g. "uncountable", and attempts to infer from its everyday usage its mathematical meaning. That such-and-such is uncountable means for Blumschein that it doesn't have the nature of a number, or something like that. So integers are "countable" for Blumschein, whereas irrationals are swimming in that sauce Weyl spoke about (but not meaning what Blumschein thinks) and therefore are "uncountable" in Blumscheins weird view. For Blumschein, your explanations are just your prejudices. It is pointless to repeat them. He can't understand you. Ralf
From: Dik T. Winter on 5 Dec 2006 19:14 In article <4575B6E1.4010505(a)et.uni-magdeburg.de> Eckard Blumschein <blumschein(a)et.uni-magdeburg.de> writes: > On 12/5/2006 2:45 PM, Dik T. Winter wrote: > > > > I wonder why the mathematicians believe to require one-point > > > compactification. I consider the rationals as genuine numbers, being as > > > close as you like to the fictions infinity and real numbers. The exact > > > numerical representation of pi requires the fiction of actual infinity. > > > > I wonder why you are talking about things you know nothing about? Who > > requires one-point compactification with what goal? > > When I presented ideas in connection with > http://iesk.et.uni-magdeburg.de/~blumsche/M283.html > I faced scepticism or refusal as well as the hint to compactification. Sorry, I can't read Word documents (I have no reader available). But again who requires one-point compactification with what goal? > I consider my ideas still flawless. I even found plausible answers to > several questions no mathematician was able to provide a convincing > answer to. So I doubt about fundamentals which require compactification. I understand that no mathematician was able to provide an answer that could convinve you. -- dik t. winter, cwi, kruislaan 413, 1098 sj amsterdam, nederland, +31205924131 home: bovenover 215, 1025 jn amsterdam, nederland; http://www.cwi.nl/~dik/
From: Virgil on 5 Dec 2006 20:05 In article <1165345832.735910.255620(a)79g2000cws.googlegroups.com>, "MoeBlee" <jazzmobe(a)hotmail.com> wrote: > Bob Kolker wrote: > > There is no such thing as a countable integer, countable rational or > > countable real. > > In the sense you're trying to get across to the other poster, I > understand your point. But, just for the record, in a technical sense > in set theory, as integers, rational numbers, and real numbers are > themselves sets, it does make sense to say whether one of them is > countable or not. For example, where integers are defined as > equivalence classes of natural numbers, each integer is itself a > denumerable set. I am not necessarily endorsing anything the other > poster has said; I'm just adding the technical note that in a strict > set theoretic sense, even numbers are sets and thus it is meaningful to > talk about the cardinality of a number. > > MoeBlee In that particular sense, each real number as a Dedekind cut, being a partition of the rationals into two sets, always has cardinality 2, while each member of a Dedekind cut is countably infinite. But each real number as a set of equivalent Cauchy sequencesis uncountable.
From: cbrown on 5 Dec 2006 20:51
Dik T. Winter wrote: > In article <4575B6E1.4010505(a)et.uni-magdeburg.de> Eckard Blumschein <blumschein(a)et.uni-magdeburg.de> writes: > > On 12/5/2006 2:45 PM, Dik T. Winter wrote: > > > > > > I wonder why the mathematicians believe to require one-point > > > > compactification. I consider the rationals as genuine numbers, being as > > > > close as you like to the fictions infinity and real numbers. The exact > > > > numerical representation of pi requires the fiction of actual infinity. > > > > > > I wonder why you are talking about things you know nothing about? Who > > > requires one-point compactification with what goal? > > > > When I presented ideas in connection with > > http://iesk.et.uni-magdeburg.de/~blumsche/M283.html > > I faced scepticism or refusal as well as the hint to compactification. > > Sorry, I can't read Word documents (I have no reader available). > But again who requires one-point compactification with what goal? > His paper "Adaptation of Spectral Analysis to Reality" doesn't contain the word "compactification" (or even the fragment "compact"). It seems to promote the use of only the real parts of a Fourier Transform (because complex values have no "physical reality"; even negative values are suspect at best) and restricting the time domain to be (-oo, 0] (because we only know the past and cannot claim to know the future). >From the paper: "7 Mathematical peculiarities In order to benefit from complete removal of redundancy, one has to restrict the field of all real numbers R to the field R+ of positive ones. Mathematics largely neglected R+ so far. Important operations like convolution are nonetheless known to be valid within R+, too. What was the function of time in R, travels outward relative to the zero of elapsed time. It is permanently incremented at zero. Integration and its reverse do no add or remove a constant of integration. Backward-ramp, down-step and singular point constitute a new unified set of singularity functions with belonging elementary spectra. " And so on. Cheers - Chas |